Question: Solve for $x$ and $y$ using elimination. ${-3x+3y = -6}$ ${-5x-3y = -50}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. $-8x = -56$ $\dfrac{-8x}{{-8}} = \dfrac{-56}{{-8}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-3x+3y = -6}\thinspace$ to find $y$ ${-3}{(7)}{ + 3y = -6}$ $-21+3y = -6$ $-21{+21} + 3y = -6{+21}$ $3y = 15$ $\dfrac{3y}{{3}} = \dfrac{15}{{3}}$ ${y = 5}$ You can also plug ${x = 7}$ into $\thinspace {-5x-3y = -50}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ - 3y = -50}$ ${y = 5}$